The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. No. The events cannot occur together. Yes. The events can occur together. No. The probability of drawing a specific second card depends on the identity of the first card. (b) Find P(ace on 1st card and ten on 2nd). (Enter your answer as a fraction.) (c) Find P(ten on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a ten in either order. (Enter your answer as a fraction.)
Added by Cory W.
Close
Step 1
Since we are not replacing the first card before drawing the second, the number of cards in the deck is reduced to 51 after the first draw, which affects the probability of the second draw. (b) Show more…
Show all steps
Your feedback will help us improve your experience
Keerti J and 55 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? No. The probability of drawing a specific second card depends on the identity of the first card.No. The events cannot occur together. Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card.Yes. The events can occur together. (b) Find P(ace on 1st card and nine on 2nd). (Enter your answer as a fraction.) (c) Find P(nine on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a nine in either order. (Enter your answer as a fraction.)
Audrey F.
The following question involves a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four 10s, etc., down to four 2s in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? Yes. The probability of drawing a specific second card is the same regardless of the identity of the first drawn card. No. The probability of drawing a specific second card depends on the identity of the first card. No. The events cannot occur together. Yes. The events can occur together. (b) Find P(ace on 1st card and jack on 2nd). (Enter your answer as a fraction.) 4/663 (c) Find P(jack on 1st card and ace on 2nd). (Enter your answer as a fraction.) (d) Find the probability of drawing an ace and a jack in either order. (Enter your answer as a fraction.) 8/663
Andrew D.
Involve a standard deck of 52 playing cards. In such a deck of cards there are four suits of 13 cards each. The four suits are: hearts, diamonds, clubs, and spades. The 26 cards included in hearts and diamonds are red. The 26 cards included in clubs and spades are black. The 13 cards in each suit are: $2,3,4,5,6,7,8,9,10,$ Jack, Queen, King, and Ace. This means there are four Aces, four Kings, four Queens, four $10 \mathrm{s},$ etc., down to four $2 \mathrm{s}$ in each deck. You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. (a) Are the outcomes on the two cards independent? Why? (b) Find $P(\text { Ace on } 1 \text { st card and } \text { King on } 2 n d)$ (c) Find $P(\text { King on 1st card and Ace on } 2 \mathrm{nd}$ ). (d) Find the probability of drawing an Ace and a King in either order.
Elementary Probability Theory
Some Probability Rules—Compound Events
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD